# Calculation of Sample Size for Survival: Logrank vs. Cox with covariates

Dear Experts; For the following Scenario, what is the best option for calculation of sample size ?

In a study with the objective to detect difference in survival between 2 treatments arms, the literature supplied contains covariates that are studied using cox regression

Option (1): Logrank test
Calculate the sample size only considering the detection of difference in survival between the two groups (referring to literature) and ignoring covariates ?

OR

Option (2) account for covariates in cox model.

Sub-option (A): Use Rule of Thumb proposed by Ogundimu, Altman and Collins 2016 recommending 20 Events per Variable.

Sub-option (B): Use “Mathematics” as in R psampsize package or NCSS PASS which require data that might have not been reported in supplied literature (e.g. the model r-squared.)

Which method seems more convenient in your opinion ?

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Rough rules of thumb such as 20 events per variable pertain to developing accurate prediction models, not to comparing groups. For comparing groups there are two main considerations: precision and power. Consideration of covariates usually requires a simulation method so most researchers take the easy way out and deal with unadjusted hazard ratios. Then calculations can be done by the R `Hmisc` package `cpower` and `spower` functions and by a lot of other software. For precision, the variance of the log odds ratio is approximately equal to the sum of the reciprocals of the number of events expected in the two groups, and from that you can easily compute the multiplicative margin of error in estimating the hazard ratio (fold change margin of error) and solve for N that makes this error below an acceptable amount.

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id do 1) Use simulations if there’re no formulae available. Do interim assessment of power if practicable

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